1. Introduction Part 1: Fundamentals 2. Symbolic Systems3. Geometric Constructions4. Spectrum of Dimensions for Recurrences Part II: Zero-Dimensional Invariant Sets 5. Uniformly Hyperbolic Repellers6. Non-Uniformly Hyperbolic Repellers7. The Spectrum for a Sticky Set8. Rhythmical Dynamics Part III: One-Dimensional Systems 9. Markov Maps of the Interval10. Suspended Flows Part IV: Measure Theoretical Results 11. Invariant Measures12. Dimensional for Measures13. The Variational Principle Part V: Physical Interpretation and Applications 14. Intuitive Explanation15. Hamiltonian Systems16. Chaos Synchronization Part VI: Appendices 17. Some Known Facts About Recurrences18. Birkhoff's Individual Theorem19. The SMB Theorem20. Amalgamation and Fragmentation Index